Can render smoke & fire in view port with [Alt A] but no fire and only smoke on render [F12]
The texture for the domain object doesn't have any coordinate mapping set. Set it to Generated. Moreover, the colour ramp is a bit off. It has to be fully transparent to the left, or the domain will be completely filled with the left colour. The left is what appears further away from the flow object and the right is what appears closer to it. Personally I prefer to have it completely transparent at the right end as well, but that is my opinion and not a requirement. At the very least, you need to flip the direction of the ramp.
  

Furthermore, the Flow type on the flow object needs to be set, depending on what you want.
  

In the image it's set to Smoke. Available options are Fire, Fire + Smoke, Smoke and Outflow.  

The first three should be self-explanatory. I have never fiddled with the outflow, but if it does the same as in the fluid sim, it should simply absorb the smoke and the flames.  

If it is set to include fire, there's also a Smoke flames section for the domain object. If you want only fire and no smoke at all, you should set Flow type to Fire and set Smoke under Smoke flames to 0.